Mathematics contains many pairs of entities that are, each in some different sense, opposites:
2 and -2 2 and 1/2
horizontal and vertical differentiation and integration
And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:
pure vs. applied (creating mathematics vs. solving problems)
teaching and learning, creating vs. teaching, arts and sciences
In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :